The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's (...) rationality. Alternatively, Y might doubt that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

Normative game theory unsatisfactorily explains rational behavior. Real people do not behave as predicted, and what is prescribed as rational behavior is normally unattainable in real-life. The problem is that current normative analysis does not account for people's cognitive limitations – their bounded rationality. However, this paper develops an account of bounded rationality that explains the rationality of more realistic behavior. I focus on the Centipede Game, in which boundedly rational players explore and test others' immediate behavior, (...) until they can apply limited backward induction. The result is that the game has a solution in the form of a subjective Nash equilibrium, which boundedly rational players can possibly realize. (shrink)

This study analyses behaviour in non-zero-sum finite multi-stage games, particularly the Centipede Game. The classical Nash Equilibrium fails to explain empirical behaviour and intuitive logic and has therefore been challenged. This paper introduces the ‘Pure Collective Equilibrium’, or PCE, which describes the equilibrium reached when agents assess their utility not by their own payoffs but by the mean collective payoff of the team, as outlined by some team-reasoning hypotheses. Classical behaviour and purely collective team reasoning then both represent (...) special cases—the first in which agents and their counterparts are on the Nash Equilibrium path, and the second in which agents and their counterparts are purely collective team reasoners. It is argued that agents intentionally and consistently deviate from classical rationality in the Centipede Game, even in the absence of philanthropic altruists or error-plagued populations. (shrink)

The partial cooperation displayed by subjects in the Centipede Game deviates radically from the predictions of traditional game theory. Even standard, infinite population, evolutionary settings have failed to provide an explanation for this behavior. However, recent work in finite population evolutionary models has shown that such settings can produce radically different results from the standard models. This paper examines the evolution of partial cooperation in finite populations. The results reveal a new possible explanation that is not open (...) to the standard models and gives us reason to be cautious when employing these otherwise helpful idealizations. *Received January 2007; revised November 2007. †To contact the author, please write to: Department of Logic and Philosophy of Science, University of California, 3151 Social Science Plaza A, Irvine, CA 92697-5100; e-mail: [email protected]. (shrink)

According to the standard objection to backward induction in games, its application depends on highly questionable assumptions about the players' expectations as regards future counterfactual game developments. It seems that, in order to make predictions needed for backward reasoning, the players must expect each player to act rationally at each node that in principle could be reached in the game, and also to expect that this confidence in the future rationality of the players would be kept by each (...) player come what may: even at the game-nodes that could only be reached by irrational play. Both expectations seem to be rather unreasonable: a player's initial disposition to rational behaviour may be weakened by a long stretch of irrational play on his part and, even more importantly, his initial confidence in the other players' future rationality may be undermined by an irrational play on their part. For different formulations of this objection see Binmore, Reny and, Bicchieri, Pettit and Sugden. and Aumann and.). (shrink)

Rational choice theory enjoys unprecedented popularity and influence in the behavioral and social sciences, but it generates intractable problems when applied to socially interactive decisions. In individual decisions, instrumental rationality is defined in terms of expected utility maximization. This becomes problematic in interactive decisions, when individuals have only partial control over the outcomes, because expected utility maximization is undefined in the absence of assumptions about how the other participants will behave. Game theory therefore incorporates not only rationality but also (...) common knowledge assumptions, enabling players to anticipate their co-players' strategies. Under these assumptions, disparate anomalies emerge. Instrumental rationality, conventionally interpreted, fails to explain intuitively obvious features of human interaction, yields predictions starkly at variance with experimental findings, and breaks down completely in certain cases. In particular, focal point selection in pure coordination games is inexplicable, though it is easily achieved in practice; the intuitively compelling payoff-dominance principle lacks rational justification; rationality in social dilemmas is self-defeating; a key solution concept for cooperative coalition games is frequently inapplicable; and rational choice in certain sequential games generates contradictions. In experiments, human players behave more cooperatively and receive higher payoffs than strict rationality would permit. Orthodox conceptions of rationality are evidently internally deficient and inadequate for explaining human interaction. Psychological game theory, based on nonstandard assumptions, is required to solve these problems, and some suggestions along these lines have already been put forward. Key Words: backward induction; Centipede game; common knowledge; cooperation; epistemic reasoning; game theory; payoff dominance; pure coordination game; rational choice theory; social dilemma. (shrink)

is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [ 4 , 5 ]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.

Two philosophical questions arise about rationality in centipede games that are logically prior to attempts to apply the formal tools of game theory to this topic. First, given that the players have common knowledge of mutual rationality and common knowledge that they are each motivated solely to maximize their own profits, is there a backwards-induction argument that employs only familiar non-technical concepts about rationality, leads to the conclusion that the first player is rationally obligated to end the (...) class='Hi'>game at the first step, is deductively valid, employs premises all of which are prima facie highly plausible, and is prima facie sound and )? Second, if there is such an argument, then is it actually sound, or is it instead defective somehow despite being prima facie sound? Addressing these two questions is our project. We present a backwards-induction argument that is prima facie sound; we argue that it is an instance of the notorious sorites paradox, and hence that the concepts of rational obligatoriness and rational permissibility are vague; and we briefly address the potential consequences of all this for the foundations of game theory and decision theory. (shrink)

I discuss how simulating another agent can be useful in some game-theoretical situations, particularly iterated games such as the centipede game.

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, (...) we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a su cient for them to play the backward induction solution in centipede games. To obtain this (...) result, we do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

At the very end of the 19th century, Gabriele Tarde wrote that all society was a product of imitation and innovation. This view regarding the development of society has, to a large extent, fallen out of favour, and especially so in those areas where the rational actor model looms large. I argue that this is unfortunate, as models of imitative learning, in some cases, agree better with what people actually do than more sophisticated models of learning. In this paper, I (...) contrast the behaviour of imitative learning with two more sophisticated learning rules (one based on Bayesian updating, the other based on the Nash-Brown-von Neumann dynamics) in the context of social deliberation problems. I show for two social deliberation problems, the Centipede game and a simple Lewis sender-receiver game, that imitative learning provides better agreement with what people actually do, thus partially vindicating Tarde. (shrink)

A puzzling finding from research on strategic decision making concerns the effect that predictions have on future actions. Simply stating a prediction about an opponent changes the total probability (pooled over predictions) of a player taking a future action as compared to not stating any prediction. These interference effects are difficult to explain using traditional economic models, and instead these results suggest turning to a quantum cognition approach to strategic decision making.

Topics in Cognitive Science, Volume 14, Issue 3, Page 492-507, July 2022.

A centipede can walk until it thinks about howit does so. Thereafter it stumbles, over thesheer impossibility of the information andcoordination required. Life in the economy islittle different. Those engaged in productionand exchange discover, pragmatically, ways tomake them work. Those observing the processsee, realistically, the immense improbabilitythat it should do so. That most economies workin practice, but must pass such toughteleological tests to succeed in theory,highlights a difference between players' andspectators' outlook which may help to explainwhy the game (...) has repeatedly been thrown wideopen just when conclusive results seemed withinreach.Section 1 of this paper identifies the fourforms of realism which economists have tendedto adopt. Section 2 considers the pragmatism ofeconomic agents, when observed in action bypsychologists and management scholars notoverly steeped in economic theory. Theconcluding section reviews the ways in whicheconomists have tried to blur the distinction,by reclassifying agents as realistic or theirown views as pragmatic, and suggests that amore pragmatic economics might bridge thedivide. (shrink)

Backward induction was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a (...) troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria. (shrink)

Through a phenomenological study of horse-human relations, this article explores the ways in which, as embodied beings, we live relationally, rather than as separate human identities. Conceptually this challenges oppositional logic and humanist assumptions, but where poststructuralist treatments of these issues tend to remain abstract, this article is concerned with an embodied demonstration of the ways in which we experience a relational or in-between logic in our everyday lives.

We argue that pedagogic authority relies on love, which is misunderstood if seen as a matter of actions and subjects. Love is based not on finite subjects and objects existing in Euclidean space and linear time, but, rather, on the non-finite ontology, space and time of relations. Loving authority is a matter of calling and vocation, arising from the spontaneous and simultaneous call-and-response of a lively relation. We make this argument through a reading of Buber’s I–You relation and Murdoch’ s (...) account of the responsiveness of ascetic discipline. In presenting this analysis, we draw upon a case study from a research project on Australian teachers and students. (shrink)

Prior research suggests brokers do not always act in the best interests of clients, although morally obligated to do so. We empirically investigated this issue focusing on trades executed at best execution price, before and after the introduction of electronic limit-order trading, on the London Stock Exchange. As a result of limit-order trading, the proportion of trades executed at the best execution price for the customer significantly increased. We attribute this to a sustained increase in the liquidity of stocks as (...) a result of limit-order trading, regardless of market capitalisation. We discuss the ethical implications of our findings and conclude that market structures that enhance market competitiveness may help reconcile broker and client interests. (shrink)

This study examined the link between employees’ adult attachment orientations and perceptions of line managers’ interpersonal justice behaviors, and the moderating effect of national culture. Participants from countries categorized as low collectivistic and high collectivistic completed an online survey. Attachment anxiety and avoidance were negatively related to interpersonal justice perceptions. Cultural differences did not moderate the effects of avoidance. However, the relationship between attachment anxiety and interpersonal justice was non-significant in the Southern Asia cultural cluster. Our findings indicate the importance (...) of ‘fit’ between cultural relational values and individual attachment orientations in shaping interpersonal justice perceptions, and highlight the need for more non-western organizational justice research. (shrink)

Abstract In this article we develop a relational understanding of sociality, that is, an account of social life that takes relation as primary. This stands in contrast to the common assumption that relations arise when subjects interact, an account that gives logical priority to separation. We will develop this relational understanding through a reading of the work of Martin Buber, a social philosopher primarily interested in dialogue, meeting, relationship, and the irreducibility and incomparability of reality. In particular, the article contrasts (...) Buber’s work with that of poststructuralist theorists who take as their starting point the deconstruction of the Hegelian logic of binary oppositions. Deconstruction understands difference as the excess that undoes the binary, but Buber, we argue, shows how difference derives from the primacy and ontological undefinability of relation. Relational logic does not exclude the logic of separations and oppositions: relation is the primal ground that makes separations possible. Content Type Journal Article Pages 1-13 DOI 10.1007/s11841-011-0278-9 Authors Andrew Metcalfe, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Ann Game, School of Social Sciences and International Studies, University of New South Wales, Sydney, NSW 2052, Australia Journal Sophia Online ISSN 1873-930X Print ISSN 0038-1527. (shrink)

Taking Arthur Fine’s The Shaky Game as my inspiration, and the recent 25th anniversary of the publication of that work as the occasion to exercise that inspiration, I sketch an alternative to the “Naturalism” prevalent among philosophers of physics. Naturalism is a methodology eventuating in a metaphysics. The methodology is to seek the deep framework assumptions that make the best sense of science; the metaphysics is furnished by those assumptions and supported by their own support of science. The alternative (...) presented here, which I call “Locavoracity,” shares Naturalism’s commitment to making sense of science, but alters Naturalism’s methodology. The Locavore’s sense-making projects are piecemeal, rather than sweeping. The Locavore’s hypothesis is that the collection of local sense-making projects fails to issue a single overarching unifying framework deserving of the title “the metaphysics that makes the best sense of science.” I muster some examples supporting the Locavore hypothesis from the interpretation of quantum field theories. (shrink)

There is an important analogy between languages and games. Just as a scoresheet records features of the evolution of a game to determine the effect of a move in that game, a conversational score records features of the evolution of a conversation to determine the effect of the linguistic moves that speakers make. Chess is particularly interesting for the study of conversational dynamics because it has language-like notations, and so serves as a simplified study in how the effect (...) of an assertion depends on, as well as evolves, the scoreboard. In this paper, we offer a compositional semantics for chess notation and a simple formal picture for determining the full information conveyed by an entry. We will also discuss an alternative model resembling accounts of centered assertion. (shrink)

A systematic introduction suitable for readers who have little familiarity with logic. Provides numerous examples and complete proofs.

We introduce the rejection game, designed to formalize the interaction between interlocutors in a Stalnakerian conversation: a speaker who asserts something and a listener who may accept or reject. The rejection game is similar to other signalling games known to the literature in economics and biology. We point out similarities and differences, and propose an application in linguistics. We uncover basic conditions under which the Gricean maxim of quality emerges from incentives among the players, providing evidence for a (...) functionalist understanding of the Gricean program. (shrink)

Recent years have witnessed an increased number of game-theoretic approaches to social norms, which apparently share some common vocabulary and methods. We describe three major approaches of this kind (due to Binmore, Bicchieri and Gintis), before comparing them systematically on five crucial themes: generality of the solution, preference transformation, punishment, epistemic conditions and type of explanation. This allows us to show that these theories are, by and large, less compatible than they seem. We then argue that those three theories (...) struggle to account for three phenomena pertaining to social norms (namely context-dependence, conflicting norms and self-evidence), with which any complete game-theoretic account should in principle be able to deal. (shrink)

Major construction projects have a great influence on the national economy and society, wherein cooperative relationship between construction suppliers plays an increasingly significant role in the overall supply chain system. However, the relationships between suppliers are noncontractual, multistage, dynamic, and complicated. To gain a deeper insight into the suppliers’ cooperative relationships, an evolutionary game model is developed to explore the cooperation tendency of multisuppliers. A replicator dynamic system is further formulated to investigate the evolutionary stable strategies of multisuppliers. Then, (...) fourteen “when-then” type scenarios are concluded and classified into six different evolutionary tracks. Meanwhile, the critical influencing factors are identified. The results show that the suppliers’ production capacity, owner-supplier contract, and the owner’s incentive mechanism influence the cooperation tendency of suppliers directly. The managerial implications contribute to insightful references for a more stable cooperative relationship between the owner and suppliers. (shrink)

The Pleadings Game is a normative formalization and computational model of civil pleading, founded in Roberty Alexy''s discourse theory of legal argumentation. The consequences of arguments and counterarguments are modelled using Geffner and Pearl''s nonmonotonic logic,conditional entailment. Discourse in focussed using the concepts of issue and relevance. Conflicts between arguments can be resolved by arguing about the validity and priority of rules, at any level. The computational model is fully implemented and has been tested using examples from Article Nine (...) of the Uniform Commercial Code. (shrink)

By means of a critical examination of a number of theses as to the nature of game-playing, the following definition is advanced: To play a game is to engage in activity directed toward bringing about a specific state of affairs, using only means permitted by specific rules, where the means permitted by the rules are more limited in scope than they would be in the absence of the rules, and where the sole reason for accepting such limitation is (...) to make possible such activity. (shrink)

In this new edition, Arthur Fine looks at Einstein's philosophy of science and develops his own views on realism. A new Afterword discusses the reaction to Fine's own theory. "What really led Einstein . . . to renounce the new quantum order? For those interested in this question, this book is compulsory reading."--Harvey R. Brown, American Journal of Physics "Fine has successfully combined a historical account of Einstein's philosophical views on quantum mechanics and a discussion of some of the philosophical (...) problems associated with the interpretation of quantum theory with a discussion of some of the contemporary questions concerning realism and antirealism. . . . Clear, thoughtful, [and] well-written."--Allan Franklin, Annals of Science "Attempts, from Einstein's published works and unpublished correspondence, to piece together a coherent picture of 'Einstein realism.' Especially illuminating are the letters between Einstein and fellow realist Schrodinger, as the latter was composing his famous 'Schrodinger-Cat' paper."--Nick Herbert, New Scientist "Beautifully clear. . . . Fine's analysis is penetrating, his own results original and important. . . . The book is a splendid combination of new ways to think about quantum mechanics, about realism, and about Einstein's views of both."--Nancy Cartwright, Isis. (shrink)

In this paper we introduce a game semantics for System P, one of the most studied axiomatic systems for non-monotonic reasoning, conditional logic and belief revision. We prove soundness and completeness of the game semantics with respect to the rules of System P, and show that an inference is valid with respect to the game semantics if and only if it is valid with respect to the standard order semantics of System P. Combining these two results leads (...) to a new completeness proof for System P with respect to its order semantics. Our approach allows us to construct for every inference either a concrete proof of the inference from the rules in System P or a countermodel in the order semantics. Our results rely on the notion of a witnessing set for an inference, whose existence is a concise, necessary and sufficient condition for validity of an inferences in System P. We also introduce an infinitary variant of System P and use the game semantics to show its completeness for the restricted class of well-founded orders. (shrink)

This paper explores the potential and relevance of an innovative sociological research method known as the Imitation Game for research in health care. Whilst this method and its potential have until recently only been explored within sociology, there are many interesting and promising facets that may render this approach fruitful within the health care field, most notably to questions about the experiential knowledge or ‘expertise’ of chronically ill patients. The Imitation Game can be especially useful because it provides (...) a way to map this experiential knowledge more systematically, without falling in the dual trap of either over-relying on in-depth, but highly specific phenomenological ‘insider’-approaches that are hard to generalize, or, alternatively, problematically reducing the rich life-worlds of patients to a set of indicators in a questionnaire. The main focus of this paper is theoretical and conceptual: explaining the Imitation Game method, discussing its usefulness in the health care domain, and exploring the ways in which the approach can be utilized for chronic illness care. The paper presents both a conceptual and empirical exploration of how the Imitation Game method and its underlying theoretical concepts of ‘contributory expertise’ and ‘interactional expertise’ can be transferred from the sociological realm to the field of health care, what kinds of insights can be gained from the method, which methodological issues it may raise, and what potentially fruitful research routes can be explored. I argue that the Imitation Game can be thought of as a ‘social learning experiment’ that simultaneously enables the participants to learn from each other’s perspectives, allows researchers to explore exciting new possibilities, and also offers the tools to intervene in the practice that is being studied. (shrink)

Hume is rightly credited with giving a brilliant, and perhaps the best, account of justice as convention. Hume's importance as a forerunner of modern economics has also long been recognized. However, most of Hume's readers have not fully appreciated how closely Hume's analysis of convention foreshadows a particular branch of economic theory, namely, game theory. Starting with the work of Barry, Runciman and Sen and Lewis, there has been a flowering of literature on the informal game-theoretic insights to (...) be found in classics of political philosophy such as Hobbes, Locke, Hume and Rousseau. A number of authors in this tradition, including Lewis, Gauthier, Mackie, and Postema, have identified passages in Hume which they interpret as giving informal examples of specific games. Yet, unlike his predecessors, Hobbes and Locke, Hume does much more than present examples which have a game-theoretic structure. In his account of convention, Hume gives general conditions which characterize the resolution of social interaction problems, and in the examples he uses to illustrate this account, Hume outlines several different methods by which agents can arrive at such a resolution. Hume's general account of convention and his explanations of the origins of particular conventions together constitute a theory of strategic interaction, which is precisely what game theory aspires to be. (shrink)

Mental representations remain the central posits of psychology after many decades of scrutiny. However, there is no consensus about the representational format(s) of biological cognition. This paper provides a survey of evidence from computational cognitive psychology, perceptual psychology, developmental psychology, comparative psychology, and social psychology, and concludes that one type of format that routinely crops up is the language-of-thought (LoT). We outline six core properties of LoTs: (i) discrete constituents; (ii) role-filler independence; (iii) predicate–argument structure; (iv) logical operators; (v) inferential (...) promiscuity; and (vi) abstract content. These properties cluster together throughout cognitive science. Bayesian computational modeling, compositional features of object perception, complex infant and animal reasoning, and automatic, intuitive cognition in adults all implicate LoT-like structures. Instead of regarding LoT as a relic of the previous century, researchers in cognitive science and philosophy-of-mind must take seriously the explanatory breadth of LoT-based architectures. We grant that the mind may harbor many formats and architectures, including iconic and associative structures as well as deep-neural-network-like architectures. However, as computational/representational approaches to the mind continue to advance, classical compositional symbolic structures – that is, LoTs – only prove more flexible and well-supported over time. (shrink)

This is a revision of game theory which takes account of agents' own descriptions of their situations, and which allows people to reason as members of groups.